Question

I receive a $1,000,000 inheritance on January 1st 2020. I cannot withdraw any of it until January 1st 2035. I plan on withdrawing the same amount each year for 30 years. How much can I withdraw each year? (Assume 8 percent interest rate).

Show all work please.

Answer 1

Annual withdrawal can be $ 281,775.64

Step-1:Future value of $ 1,000,000 on January 1st 2035
Future value	=	P*(1+i)^n		Where,
	=	1000000*(1+0.08)^15		P	=	$       10,00,000
	=	$ 31,72,169.11		i	=	8%
				n	=	15
Step-2:Calculation of annual withdrawal for 30 years
Annual withdrawal	=	Investment amount at the beginning of January 1st 2035	/	Present value of annuity of 1
	=	$ 31,72,169.11	/	11.25778
	=	$ 2,81,775.64
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.08)^-30)/0.08		i	=	8%
	=	11.25778334		n	=	30